Question: $ \left(\dfrac{256}{81}\right)^{\frac{3}{4}}$
$= \left(\left(\dfrac{256}{81}\right)^{\frac{1}{4}}\right)^{3}$ To simplify $\left(\dfrac{256}{81}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left(? \right)^{4}=\dfrac{256}{81}$ To simplify $\left(\dfrac{256}{81}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left({\dfrac{4}{3}}\right)^{4}=\dfrac{256}{81}$ so $ \left(\dfrac{256}{81}\right)^{\frac{1}{4}}=\dfrac{4}{3}$ So $\left(\dfrac{256}{81}\right)^{\frac{3}{4}}=\left(\left(\dfrac{256}{81}\right)^{\frac{1}{4}}\right)^{3}=\left(\dfrac{4}{3}\right)^{3}$ $= \left(\dfrac{4}{3}\right)\cdot\left(\dfrac{4}{3}\right)\cdot \left(\dfrac{4}{3}\right)$ $= \dfrac{16}{9}\cdot\left(\dfrac{4}{3}\right)$ $= \dfrac{64}{27}$